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Even as it’s used in English to modify “information,” either as a single one-word attributive adjective or as a single hyphenated one, I think “code[-]word” could use some help to capture more coherently the [sensitive] nature of that information.

I say this primarily because, in addition to the one you describe, I see another possible attributive use of “code[-]word” in “code[-]word information” as meaning simply/literally “information about code words,” such as a list of code words (with or without their corresponding projects/operations) currently or formerly in use by a/n [spy] agency
(cf: the attributive use of “login” or “credit card” in “Never reveal your login/credit card information!”).

In English, to distinguish it better in my mind from the “login/credit card” attributive use just mentioned above, I read “code[-]word information” in the attributive use at issue to mean either “code[-]word[-]protected information” or “code[-]word level information,” with both of which standing for “information requiring code[-]word clearance to access” and with this in mind, I’d humbly propose that it would require more than adding a simple proposition in French to coherently transform the noun “mot-code” to an attributive adjective of “information.”

Although with nothing to support me, I do think, however, that “mot-code” alone could coherently modify words like “niveau” or “habilitation” (just as I’ve used “code[-]word” to modify “level” and “clearance” in English) and perhaps even a word like “genre” (which is actually my favorite):

Thank you! It is not so much imho that the word has the ability to modify niveau/habilitation but rather that by phrasing it like so the construction lends itself to using a compound for a preposition and a determiner i.e. du and this helps smooth it so to speak. Also genre allows for this nuance about something which by virtue of its value might be destined to be, as opposed to being actually in such a state imho. Your discussion captures some of the concerns I had over using the word with not cue as to what it's supposed to "change". Well done! Cheers.
– user3177May 22 '17 at 23:22